## Geometry & Topology

### Geodesic flow for $\mathrm{CAT}(0)$–groups

#### Abstract

We associate to a $CAT(0)$–space a flow space that can be used as the replacement for the geodesic flow on the sphere tangent bundle of a Riemannian manifold. We use this flow space to prove that $CAT(0)$–group are transfer reducible over the family of virtually cyclic groups. This result is an important ingredient in our proof of the Farrell–Jones Conjecture for these groups.

#### Article information

Source
Geom. Topol., Volume 16, Number 3 (2012), 1345-1391.

Dates
Revised: 12 March 2012
Accepted: 2 June 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732439

Digital Object Identifier
doi:10.2140/gt.2012.16.1345

Mathematical Reviews number (MathSciNet)
MR2967054

Zentralblatt MATH identifier
1263.37052

Subjects
Primary: 20F67: Hyperbolic groups and nonpositively curved groups

#### Citation

Bartels, Arthur; Lück, Wolfgang. Geodesic flow for $\mathrm{CAT}(0)$–groups. Geom. Topol. 16 (2012), no. 3, 1345--1391. doi:10.2140/gt.2012.16.1345. https://projecteuclid.org/euclid.gt/1513732439

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